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Extreme water-wave profile recovery from pressure measurements at the seabed

Published online by Cambridge University Press:  28 September 2020

Didier Clamond Open the ORCID record for Didier Clamond [Opens in a new window]  and
David Henry Open the ORCID record for David Henry [Opens in a new window]
Didier Clamond*
Affiliation:
Université Côte d'Azur, CNRS UMR 7351, LJAD, Parc Valrose, 06108Nice CEDEX 2, France
David Henry
Affiliation:
Department of Applied Mathematics, University College Cork, CorkT12 XF62, Ireland
*
†Email address for correspondence: didier.clamond@univ-cotedazur.fr
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Abstract

In this note, we establish the applicability and effectiveness of a recently developed approach to the recovery of nonlinear water waves from pressure measurements by proving that it is applicable to the celebrated extreme Stokes wave.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Mathematical Foundations: General fluid mechanics
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , R3
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Amick, C. J. & Fraenkel, L. E. 1987 On the behavior near the crest of waves of extreme form. Trans. Am. Math. Soc. 299 (1), 273–298.CrossRefGoogle Scholar
Bair, J. & Haesbroeck, G. 1997 Monotonous stability for neutral fixed points. Bull. Belg. Math. Soc. 4, 639–646.CrossRefGoogle Scholar
Bishop, C. T. & Donelan, M. A. 1987 Measuring waves with pressure transducers. Coast. Engng 11, 309–328.CrossRefGoogle Scholar
Bonneton, P. & Lannes, D. 2017 Recovering water wave elevation from pressure measurements. J. Fluid Mech. 833, 399–429.CrossRefGoogle Scholar
Buffoni, B. & Toland, J. F. 2003 Analytic Theory of Global Bifurcation. Princeton University Press.CrossRefGoogle Scholar
Clamond, D. 2013 New exact relations for easy recovery of steady wave profiles from bottom pressure measurements. J. Fluid Mech. 726, 547–558.CrossRefGoogle Scholar
Clamond, D. 2017 Remarks on Bernoulli constants, gauge conditions and phase velocities in the context of water waves. Appl. Maths Lett. 74, 114–120.CrossRefGoogle Scholar
Clamond, D. 2018 New exact relations for steady irrotational two-dimensional gravity and capillary surface waves. Phil. Trans. R. Soc. A 376 (2111), 20170220.CrossRefGoogle ScholarPubMed
Clamond, D. & Constantin, A. 2013 Recovery of steady periodic wave profiles from pressure measurements at the bed. J. Fluid Mech. 714, 463–475.CrossRefGoogle Scholar
Constantin, A. 2006 The trajectories of particles in Stokes waves. Invent. Math. 166, 523–535.CrossRefGoogle Scholar
Constantin, A. 2011 Nonlinear water waves with applications to wave-current interactions and tsunamis. CBMS-NSF Conference Series in Applied Mathematics, vol. 81. SIAM.CrossRefGoogle Scholar
Constantin, A. 2012 a Particle trajectories in extreme Stokes waves. IMA J. Appl. Maths 77 (3), 293–307.CrossRefGoogle Scholar
Constantin, A. 2012 b On the recovery of solitary wave profiles from pressure measurements. J. Fluid Mech. 699, 373–384.CrossRefGoogle Scholar
Constantin, A. 2016 Exact travelling periodic water waves in two-dimensional irrotational flows. In Nonlinear Water Waves (ed. Constantin, A.), Lecture Notes in Mathematics, vol. 2158, pp. 1–82, Springer.CrossRefGoogle Scholar
Constantin, A. & Strauss, W. 2010 Pressure beneath a Stokes wave. Commun. Pure Appl. Maths 63, 533–557.Google Scholar
Escher, J. & Schlurmann, T. 2008 On the recovery of the free surface from the pressure within periodic traveling water waves. J. Nonlinear Math. Phys. 15, 50–57.CrossRefGoogle Scholar
Grant, M. A. 1973 The singularity at the crest of a finite amplitude progressive Stokes wave. J. Fluid Mech. 59 (2), 257–262.CrossRefGoogle Scholar
Henry, D. 2011 Pressure in a deep-water Stokes wave. J. Math. Fluid Mech. 13 (2), 251–257.CrossRefGoogle Scholar
Henry, D. & Thomas, G. P. 2018 Prediction of the free-surface elevation for rotational water waves using the recovery of pressure at the bed. Phil. Trans. R. Soc. A 376 (2111), 20170102.CrossRefGoogle Scholar
Longuet-Higgins, M. S. & Fox, M. J. H. 1977 Theory of the almost-highest wave: the inner solution. J. Fluid Mech. 80 (4), 721–741.CrossRefGoogle Scholar
Lyons, T. 2016 The pressure distribution in extreme Stokes waves. Nonlinear Anal. Real World Appl. 31, 77–87.CrossRefGoogle Scholar
McLeod, J. B. 1987 The asymptotic behavior near the crest of waves of extreme form. Trans. Am. Math. Soc. 299 (1), 299–302.CrossRefGoogle Scholar
Norman, A. C. 1974 Expansions for the shape of maximum amplitude Stokes waves. J. Fluid Mech. 66 (2), 261–265.Google Scholar
Oliveras, K. L., Vasan, V., Deconinck, B. & Henderson, D. 2012 Recovering surface elevation from pressure data. SIAM J. Appl. Maths 72 (3), 897–918.CrossRefGoogle Scholar
Schwartz, L. W. & Fenton, J. D. 1982 Strongly nonlinear waves. Annu. Rev. Fluid Mech. 14, 39–60.CrossRefGoogle Scholar
Stokes, G. G. 1880 Considerations relative to the greatest height of oscillatory waves which can be propagated without change of form. Math. Phys. Papers 1, 225–228.Google Scholar
Toland, J. F. 1996 Stokes waves. Topol. Meth. Nonlinear Anal. 7, 1–48.CrossRefGoogle Scholar
Tsai, C. H., Huang, M. C., Young, F. J., Lin, Y. C. & Li, H. W. 2005 On the recovery of surface wave by pressure transfer function. Ocean Engng 32, 1247–1259.CrossRefGoogle Scholar